Detective Superintendent Richard Baker said: “This is a tragic case and the victim’s family are devastated.

“I would urge the public not to approach the man but to immediately dial 999. We have officers ready to respond immediately to sightings.”

Police said they were alerted at 7.37am when the bus driver on the number nine route reported that a passenger had been wounded. She had been on the top deck of the bus.

Det Supt Baker said the girl was believed to be on her way to school. Her family were “extremely distressed and distraught”. Specially-trained family liaison officers were with them.

“The girl had been on the bus for a short period of time when the incident occurred,” he added. “It appears to have been quite a sporadic and very quick attack on the girl.”

He said police were investigating the possibility the murder was a random attack, adding: “We’re looking at a number of motives at the moment.”

Det Supt Baker added: "I'm not able to say with any kind of certainty if the suspect was known to the offender."

He warned people not to approach the suspect. It was believed he might still be carrying a weapon.

“He is believed to be dangerous,” he said. “I am confident that we will catch the individual responsible.”

The suspect was said to be wearing a dark-coloured hooded top with a “very distinctive” tiger or leopard motif on the back. Initial descriptions suggested he had a bandage on his right hand or was carrying a small white bag.

The officer added: “We are utilising every specialist officer, local policing officers and investigators in order to identify, locate and arrest the offender who is currently outstanding.”

Police have interviewed pasengers who were on the bus but have urged others to come forward. No other passengers were injured in the stabbing incident.

Forensic teams conducted a fingertip search of the bus before it was taken to a police compound at 11.45am.

A man was detained today by police in connection with the incident but later released without being arrested.

A police spokesman said: “Police were alerted to the incident at 7.37am when the bus driver reported that a passenger had been wounded.

“Officers and other emergency services were immediately dispatched but despite valiant efforts to save the teen it was clear that this was a fatal attack.

“Officers who flooded the scene and spoke to witnesses remain at the location near to the Morrisons supermarket on Hagley Road.

“The out of city stretch of Hagley Road is likely to remain closed for the rest of the day and drivers and pedestrians should avoid the area until further notice.

“Officers from across the force − supported by police dog handlers, firearms officers, transport police and others − are searching for the person responsible.”

West Midlands Ambulance Service said it was called to an emergency on board a bus in Edgbaston shortly after 7.35am.

A spokesman said: “A senior paramedic officer in a rapid response vehicle, two Basics (British Association for Immediate Care) emergency medics and two ambulance crews attended. One person was confirmed dead at the scene.”

The stabbing took place on a stretch of the road between a Morrisons supermarket at Tricorn House, an office block.

Early reports about the attack emerged on social networking sites. Darren Bent wrote: “Can’t believe some guy has just stabbed and killed a school girl right in front of my missus on the number nine bus on her way to work and she had to give CPR love you xxx the guy did it as bus was about to stop and ran off.”